A Gentle Introduction to PythonTEX

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A Gentle Introduction to

PythonTEX Andrew Mertz, William Slough Overview A Question of Primes Introduction to PythonTEX Mathematics with Sympy Plots with matplotlib Web Services Conclusions Extra Examples

A Gentle Introduction to PythonTEX

Andrew Mertz

William Slough

Mathematics and Computer Science Department

Eastern Illinois University

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PythonTEX

Andrew Mertz, William Slough

Overview A Question of Primes Introduction to PythonTEX Mathematics with Sympy Plots with matplotlib Web Services Conclusions Extra Examples

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PythonTEX

Python Overview

◮

General purpose, high-level programming language

◮

Multi-paradigm: object-oriented, imperative, functional

◮

Comprehensive standard library

◮

Origins from late 1989

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PythonTEX

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PythonTEX

A Recent Question on TEX Stack Exchange

“I would like to write a L

A

_{TEX script that produces all the prime}

numbers between the numbers

n

and

m

, where

n

<

_m

. How can I do

this? I feel it should not be that hard, but I cannot seem to program

it.”

— Kevin

†

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PythonTEX

From The TEXBook, Page 218 (1984)

The first 30 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,

37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107,

109, and 113. You may not find this fact very startling; but you may

be surprised to learn that the previous sentence was typeset by saying

The first thirty prime numbers are \primes{30}.

TEX did all the calculation by expanding the

primes

macro, so the

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PythonTEX

Knuth’s Code,

-worthy

\newif\ifprime \newif\ifunknown % boolean variables

\newcount\n \newcount\p \newcount\d \newcount\a % integer variables

\def\primes#1{2,~3% assume that #1 is at least 3

\n=#1 \advance\n by-2 % n more to go

\p=5 % odd primes starting with p

\loop\ifnum\n>0 \printifprime\advance\p by2 \repeat}

\def\printp{, % we will invoke \printp if p is prime

\ifnum\n=1 and~\fi % and precedes the last value

\number\p \advance\n by -1 }

\def\printifprime{\testprimality \ifprime\printp\fi}

\def\testprimality{{\d=3 \global\primetrue

\loop\trialdivision \ifunknown\advance\d by2 \repeat}}

\def\trialdivision{\a=\p \divide\a by\d

\ifnum\a>\d \unknowntrue\else\unknownfalse\fi

\multiply\a by\d

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PythonTEX

David Carlisle’s Response

\makeatletter

\def\primes#1#2{{%

\def\comma{\def\comma{, }}%

\count@\@ne\@tempcntb#2\relax\@curtab#1\relax

\@primes}}

\def\@primes{\loop\advance\count@\@ne

\expandafter\ifx\csname p-\the\count@\endcsname\relax

\ifnum\@tempcntb<\count@\else

\ifnum\count@<\@curtab\else\comma\the\count@\fi\fi\else\repeat

\@tempcnta\count@\loop\advance\@tempcnta\count@

\expandafter\let\csname p-\the\@tempcnta\endcsname\@ne

\ifnum\@tempcnta<\@tempcntb\repeat

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PythonTEX

Karl Koeller’s Response

A solution using the

\pgfmathisprime

macro provided by Alain

Matthes’

tkz-euclide

package:

\usepackage{tkz-euclide}

\newif\ifcomma

\newcommand{\primes}[2]{%

\commafalse%

\foreach\numb in {#1,...,#2}{%

\pgfmathisprime{\numb}%

\ifnum\pgfmathresult=1

\ifcomma, \numb\else\numb\global\commatrue\fi%

\fi%

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PythonTEX

Can PythonTEX Make This Simpler?

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PythonTEX

Evaluating Expressions With

\py

The macro

\py{expression}

evaluates a Python expression and

typesets its

value

.

Did you know that $2^{65} = \py{2**65}$?

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PythonTEX

Evaluating Expressions With

\pyc

The macro

\pyc{expression}

evaluates a Python expression and

typesets anything that it

prints

.

Did you know that $2^{65} = \pyc{print(2**65)}$?

Did you know that 2

65 _{= 36893488147419103232?}

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PythonTEX

A More Complex Example Using

\pyc

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PythonTEX

Charleston, Illinois USA

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PythonTEX

Generating Tables With

pycode

\begin{pycode}

print(r"\begin{tabular}{c|c}")

print(r"$m$ & $2^m$ \\ \hline")

print(r"%d & %d \\" % (1, 2**1))

print(r"%d & %d \\" % (2, 2**2))

print(r"%d & %d \\" % (3, 2**3))

print(r"%d & %d \\" % (4, 2**4))

print(r"\end{tabular}")

\end{pycode}

\begin{tabular}{c|c}

$m$ & $2^m$ \\ \hline

1 & 2 \\

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PythonTEX

Generating Tables With

pycode

\begin{pycode}

print(r"\begin{tabular}{c|c}")

print(r"$m$ & $2^m$ \\ \hline")

print(r"%d & %d \\" % (1, 2**1))

print(r"%d & %d \\" % (2, 2**2))

print(r"%d & %d \\" % (3, 2**3))

print(r"%d & %d \\" % (4, 2**4))

print(r"\end{tabular}")

\end{pycode}

m

2 m

1

2

4

3

8

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PythonTEX

Generating Tables With a Loop

\begin{pycode}

lo, hi = 1, 6

print(r"\begin{tabular}{c|c}")

print(r"$m$ & $2^m$ \\ \hline")

for m in range(lo, hi + 1):

print(r"%d & %d \\" % (m, 2**m))

print(r"\end{tabular}")

\end{pycode}

m

2 m

1

2

4

3

8

4

16

5

32

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PythonTEX

Defining a Function

\begin{pycode}

def fib(n):

# nth Fibonacci value

a, b = 0, 1

for i in range(n):

a, b = b, a + b

return a

\end{pycode}

Did you know that $F_{10} = \py{fib(10)}$?

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PythonTEX

Sessions

py

,

pyc

, and

pycode

all have an optional

session

argument.

This argument determines the name of the Python session in which

the code is executed.

Sessions with different names may be executed in parallel providing a

speedup.

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PythonTEX

Introducing

pythontexcustomcode

\begin{pythontexcustomcode}{py}

def makeTable(lo, hi):

print(r"\begin{tabular}{c|c}")

print(r"$m$ & $2^m$ \\ \hline")

for m in range(lo, hi + 1):

print(r"%d & %d \\" % (m, 2**m))

print(r"\end{tabular}")

\end{pythontexcustomcode}

The

pythontexcustomcode

environment evaluates the code block

at the start of each “session” – which makes it a great place to

define well-tested functions.

\begin{pythontexcustomcode}{py}

python code block

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PythonTEX

Generating Tables in Multiple Sessions

\pyc[table1]{makeTable(1, 4)}

m

2 m

1

2

4

3

8

4

16 \pyc[table2]{makeTable(4, 10)}

m

2 m

4

16

5

32

6

64

7

128

8

256

9

512

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PythonTEX

Generating Tables From a Function

\begin{pythontexcustomcode}{py}

def makeTableFromFunction(lo, hi, funct, label):

print(r"\begin{tabular}{c|c}")

print(r"$m$ & %s \\ \hline" % label)

for m in range(lo, hi + 1):

print(r"%d & %d \\" % (m, funct(m)))

print(r"\end{tabular}")

\end{pythontexcustomcode}

\pyc{makeTableFromFunction(7, 11, fib, "$F_{m}$")}

m

F

m

7

13

8

21

9

34

10

55

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PythonTEX

Generating Tables From a Library Function

Python excels in the quantity and quality of its modules.

Modules make additional functions available. To use them, the

corresponding module needs to be imported.

\begin{pythontexcustomcode}{py}

import math

\end{pythontexcustomcode}

\pyc{makeTableFromFunction(30, 33, math.factorial, "$m!$")}

m

!

30 265252859812191058636308480000000

31 8222838654177922817725562880000000

32 263130836933693530167218012160000000

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PythonTEX

Generating Tables From a Library Function

With the import statement the module name is needed each time a

member of the module is used.

To avoid this, a

from import

statement can be used.

This can shadow other functions and should be used with care.

\begin{pythontexcustomcode}{py}

from math import factorial

\end{pythontexcustomcode}

\pyc{makeTableFromFunction(30, 33, factorial, "$m!$")}

m

!

30 265252859812191058636308480000000

31 8222838654177922817725562880000000

32 263130836933693530167218012160000000

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PythonTEX

Remember Kevin?

\begin{pythontexcustomcode}{py}

from sympy import prime

def generatePrimes(n):

# Assume n >= 3

for i in range(1, n):

print("%d, "

% prime(i))

print("and %d%%" % prime(n))

\end{pythontexcustomcode}

The first 30 primes are \pyc{generatePrimes(30)}.

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PythonTEX

Processing PythonTEX Files

1. pdfL

A

_TEX

_{2. pythonTEX}

_{3. pdfL}

A

_TEX

my.tex

my.pytxcode

pythontex-files-my

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PythonTEX

Symbolic Mathematics With Sympy

>>>

from

sympy

import

*

>>>

var("x, y")

# Define symbolic variables

(x, y)

>>>

z

=

(x

+

y)

**3

# Define an expression

>>>

z

# Display z

(x + y)**3

>>>

expand(z)

# Display the expansion of z

x**3 + 3*x**2y + 3x*y2 + y3

>>>

latex(expand(z))

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PythonTEX

Expanding Binomials

\begin{pycode}

from sympy import *

var("x, y")

binomials = []

for m in range(3, 6):

binomials.append((x + y)**m)

print(r"\begin{align*}")

for expr in binomials:

print(r"%s &= %s\\" % (latex(expr), latex(expand(expr))))

print(r"\end{align*}")

\end{pycode}

(

x

+

y

)

3 =

x

3 + 3

x

2 y

+ 3

xy

2 +

y

3 (

x

+

y

)

4 =

x

4 + 4

x

3 y

+ 6

x

2 y

2 + 4

xy

3 +

y

4

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PythonTEX

A Little Bit of Calculus

\begin{pycode}

functions = [sin(x), cos(x), tan(x)]

print(r"\begin{align*}")

for f in functions:

d = Derivative(f, x)

print(latex(d) + "&=" + latex(d.doit()) + r"\\")

print(r"\end{align*}")

\end{pycode}

d

dx

sin (

x

) = cos (

x

)

d

dx

cos (

x

) =

−

sin (

x

)

d

dx

tan (

x

) = tan

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PythonTEX

A Little Bit More

\begin{pycode}

functions = [sin(x), cos(x), tan(x)]

print(r"\begin{align*}")

for f in functions:

i = Integral(f, x)

print(latex(i) + "&=" + latex(i.doit()) + r"\\")

print(r"\end{align*}")

\end{pycode}

Z

sin (

x

)

dx

=

−

cos (

x

)

Z

cos (

x

)

dx

= sin (

x

)

Z

tan (

x

)

dx

=

−

1

2 log sin

2 ₍

x

)

−

1

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A Gentle Introduction to PythonTEX Andrew Mertz, William Slough Overview A Question of Primes Introduction to PythonTEX Mathematics with Sympy Plots with matplotlib Web Services Conclusions Extra Examples

Stirling’s Triangle

Stirling’s Triangle for Subsets

n

0 n

1 n

2 n

3 n

4 n

5 n

6 n

7 n

8

0

1

0

1

2

0

1

3

0

1

3

1

4

0

1

7

6

1

5

0

1

15

25

10

1

6

0

1

31

90

65

15

1

7

0

1

63

301

350

140

21

1

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PythonTEX

Stirling’s Triangle (code excerpt)

from sympy.functions.combinatorial.numbers import *

for n in range(numberOfRightHandColumns):

print("%d" % n)

for k in range(n + 1):

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A Gentle Introduction to PythonTEX Andrew Mertz, William Slough Overview A Question of Primes Introduction to PythonTEX Mathematics with Sympy Plots with matplotlib Web Services Conclusions Extra Examples

Plotting With Matplotlib

0

1

2

3

4

5 time (s)

−

0 .

8 −

0 .

6 −

0 .

4 −

0 .

2

0 .

0

0 .

2

0 .

4

0 .

6

0 .

8

1 .

0 v

o

lt

a

g

e

(m

V

)

y

= cos(2

πt

)

e

−

t

Damped exponential decay

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PythonTEX

Plot Details, Part 1

\begin{pycode}

from pylab import *

# Define f(t), the desired function to plot

def f(t):

return cos(2 * pi * t) * exp(-t)

# Generate the points (t_i, y_i) to plot

t = linspace(0, 5, 500)

y = f(t)

# Begin with an empty plot, 5 x 3 inches

clf()

figure(figsize=(5, 3))

# Use TeX fonts

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PythonTEX

Plot Details, Part 2

# Generate the plot with annotations

plot(t, y)

title("Damped exponential decay")

text(3, 0.15, r"$y = \cos(2 \pi t) e^{-t}$")

xlabel("time (s)")

ylabel("voltage (mV)")

# Save the plot as a PDF file

savefig("myplot.pdf", bbox_inches="tight")

# Include the plot in the current LaTeX document

print(r"\begin{center}")

print(r"\includegraphics[width=0.85\textwidth]{myplot.pdf}")

print(r"\end{center}")

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PythonTEX

Simple Access of a Web Service

Many powerful and freely available web services can be accessed

though the libraries of Python.

Python has excellent JSON, XML and networking libraries.

The first web service we will use is Google’s Geocoding API.

Geocoding is the process of converting an address into geographic

coordinates such as latitude and longitude.

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PythonTEX

Using Google’s Geocoding Service

from urllib2 import urlopen

from urllib import urlencode

import json

def findLatlong(address):

# Build the data needed to call the Goggle API

query = {"address": address, "sensor": "false"}

data = urlencode(query)

url = "http://maps.googleapis.com/maps/api/geocode/json?"

url += data

# Fetch and parse

result = json.load(urlopen(url))

latlong = result["results"][0]["geometry"]["location"]

return (latlong["lat"], latlong["lng"])

The latitude and longitude of Tokyo is \py{findLatlong("Tokyo")}

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PythonTEX

Executing a Subprocess

Python can run other programs and use their output.

Here we use

webkit2png

to render a web page as an image that is

included in the document.

import subprocess

def showWebpage(url, filename):

subprocess.call(["webkit2png", "-o", filename,

"-F", "javascript",

"-w", "5",

url])

print(r"\begin{center}")

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PythonTEX

How the Maps Were Made (pseudocode)

def showGoogleMap(address, zoomlevel):

# Find the latitude and longitude of the address

# Build a web page with the JavaScript needed to load

# a Google Map at the given location and zoom level

# Save the web page to a temporary file

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PythonTEX

Issues

◮

PythonTEX adds significant processing time

Appropriate use of sessions can reduce this time, but

there is still a large overhead.

◮

Debugging Python code within TEX is difficult

Test complex Python code outside of TEX first

◮

TEX macros that have arguments generated by Python fail on

first processing step

Add such TEX macros from within Python

◮

Use parentheses for print statements:

_print(x)

.

◮

Be clear of the differences between

_\py

and

_\pyc

.

◮

When using Beamer use the frame option

fragile=singleslide

if able.

◮

Be skeptical of SymPy results.

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PythonTEX

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PythonTEX

References

Python:

python.org

SciPy:

scipy.org

PythonTEX(Geoffrey Poore):

www.ctan.org/pkg/pythontex

Anaconda(Python distribution):

store.continuum.io/cshop/anaconda

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PythonTEX

How to Shorten a Long URL

from urllib2 import Request

def shortenURL(longURL):

# Build the data needed to call the Goggle API

url = "https://www.googleapis.com/urlshortener/v1/url"

query = {"longUrl": longURL, "key": googleAPIKey}

data = json.dumps(query)

request = Request(url, data,

{"Content-Type": "application/json"})

# Fetch and parse

result = json.load(urlopen(request))

shortURL = result["id"]

print(r"\url{%s}%%" % shortURL)

Here is a short url \pyc{shortenURL(

"http://mirror.jmu.edu/pub/CTAN/macros/latex/contrib/pythontex/pythontex.pdf"

)}

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PythonTEX

Mail Merge

Address:

to field

Hello

name field

, I just wanted to say hello.

to,name

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PythonTEX

Mail Merge

\begin{pythontexcustomcode}{py}

import csv

def mailMerge(filename, texcommand):

csvFile = open(filename, "r")

csvReader = csv.DictReader(csvFile)

for row in csvReader:

setCommand = r"\def\mail%s{%s}"

for keyValuePair in row.items():

print(setCommand % keyValuePair)

print(r"%s\vfill" % texcommand)

\end{pythontexcustomcode}

\newcommand{\mailBody}{

Address: \mailto\\

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PythonTEX

Mail Merge

\pyc{mailMerge("../data.csv", r"\mailBody")}

Address: js@example.com

Hello John Smith, I just wanted to say hello.

Address: mw@example.com

Hello Mike White, I just wanted to say hello.

Address: tb@example.com

A Gentle Introduction to PythonTEX